US7343275B2 - Method for modelling the production of hydrocarbons by a subsurface deposit which are subject to depletion - Google Patents

Method for modelling the production of hydrocarbons by a subsurface deposit which are subject to depletion Download PDF

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US7343275B2
US7343275B2 US10/508,206 US50820604A US7343275B2 US 7343275 B2 US7343275 B2 US 7343275B2 US 50820604 A US50820604 A US 50820604A US 7343275 B2 US7343275 B2 US 7343275B2
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reservoir
gas
depletion
transfer coefficient
model
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US20050165593A1 (en
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Roland Lenormand
Fabrice Bauget
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B49/00—Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells

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  • the present invention relates to a method for modelling the production of hydrocarbons comprising notably relatively high-viscosity oils by petroleum reservoirs subjected to decompression or depletion.
  • Pore network models are also known, which are notably described by Li, X., Yortsos, Y. C., 1991 , Visualization and Numerical Studies of Bubble Growth during Pressure Depletion , SPE 22589 66 th Annual Technical Conference and Exhibition, Dallas, Tex., October 6-9, based on a pore-scale physics and which therefore cannot simulate an experiment on the scale of a core and take into account of the boundary conditions specific to the experiments. These models have been tested only for light oils and they do not take into account dispersed gas flow.
  • the method according to the invention allows, from laboratory measurements on such samples and by means of suitable corrections described hereafter, realistic modelling of the production of a depleted reservoir, whatever the viscosity of the oils produced, and more particularly when it contains viscous oils, by using a commercially available compositional reservoir simulator.
  • the modelling method according to the invention allows simulation of production by an underground reservoir under the effect of depletion. It affords an excellent compromise between the accuracy to the physical mechanisms and modelling simplicity, in particular a small number of parameters that can be determined from a single laboratory experiment.
  • the method essentially comprises the following stages:
  • the gas fraction flow model is essentially described by a parameter F characterizing the force required for untrapping the bubbles; a parameter ⁇ characterizing the change of the gas phase to the continuous form, the two parameters being determined by calibration from the laboratory measurements, and by the values of the relative permeability to the continuous gas fraction.
  • the transfer is modelled by a volume transfer coefficient which has meaning on the laboratory scale and on the reservoir scale, whose dependence has been expressed as a function of the various parameters: gas saturation, oversaturation, liquid velocity.
  • FIG. 1 illustrates the principle of a petroleum reservoir production simulation, the main useful parameter being the relative permeability which expresses the interactions between the fluids (water, oil or gas) and the rock;
  • FIG. 2 shows, for water or gas drive methods, the experimental scheme allowing obtaining, from measurements on samples, relative permeabilities Kr suitable at the laboratory stage as well as in the reservoirs;
  • FIG. 3 illustrates the principle of determination of the characteristic parameters of flow of an oil by depletion from laboratory experiments, which is the object of the first essential stage of the method
  • FIG. 4 shows the principle of use of a flow simulator for carrying out a numerical experiment under reservoir conditions allowing determination of “reservoir Kr” values, which is the object of the second essential stage of the method;
  • FIG. 5 diagrammatically shows the various “pseudo”-stages present in the porous medium (the residual water phase is not mentioned but it exists;
  • FIG. 6 shows simulation examples for a light C 1 -C 3 -C 10 oil
  • FIGS. 7 and 8 show a first series of simulations carried out for different viscous oils (250 cp and 3300 cp) in the same rock type.
  • FIGS. 9 and 10 show a second series of simulations, the first one with an oil whose viscosity is about 1500 cp at 0.5 and 12 bar ⁇ j ⁇ 1 , the second with an oil whose viscosity is about 300 cp at 0.8 and 8 bar ⁇ j ⁇ .
  • a first important point of the method of the invention relates to the “off-equilibrium” aspect of the light component transfer. It is based on modelling of the gas phase nucleation allowing prediction of the density of the bubbles and the pressure at which they appear. A law of distribution of the number of pre-existing “nuclei” or microbubbles as a function of the pressure is suggested. This empirical law N(P) takes into account the properties of the solid (surface roughness), the properties of the fluids and the physico-chemical interactions between the fluids and the solid (wettability for example). A relation form, for example exponential or power law, is imposed from the published measurements and the few parameters of this law (threshold pressure, exponent of the power law) are determined from the experiment by calibration.
  • the method comprises a computing stage allowing determination of the transfer between the phase of the light component between the liquid and the gas. This computation takes into account the off-equilibrium difference and it therefore allows prediction of the evolution of the gas production with time, for any depletion rate.
  • the second point of the modelling method relates to the flow of the gas in a non-continuous form.
  • Three possible situations for the gas are distinguished: either a phase trapped in form of bubbles or “bubble strings”, or a mobile dispersed phase carried along by the oil flow, or a continuous phase flowing according to the conventional laws relative to flows in porous media (Darcy's law).
  • the method allows producing a gas flow model described by a very small number of parameters that can be either calibrated on depletion experiments or measured separately:
  • a parameter F characterizing the force required for bubble untrapping (adhesion to the walls or capillary trapping), to be determined by calibration
  • the flow model allows calculation of the flow properties (critical saturations, gas flow, etc.) as a function of constants F and ⁇ , of the properties of the fluids and of the experimental conditions (velocity of flow, depletion rate, etc.).
  • Coupling of the transfer model with the flow model allows simulation of an experiment in any condition. It is used in two stages respectively illustrated by FIGS. 3 and 4 :
  • a fluid volume V (liquid+gas) is considered.
  • the pressure in the gas is P.
  • the total surface area of the bubbles in this volume is denoted by s and N 0 is the total number of bubbles per volume unit of fluid. All the bubbles are assumed to have the same radius r.
  • V G N 0 ⁇ V ⁇ 4 ⁇ ⁇ ⁇ ⁇ r 3 3 ( 2 )
  • the radius can be eliminated by expressing the surface area as a function of the volume:
  • An estimation of the surface transfer coefficient h s can be given by replacing the gradient at the wall in the local approach by a mean gradient, using the mean distance d between bubbles:
  • Equation (11) The dimension of h v is (time) ⁇ 1 .
  • volume transfer coefficient h v first depends on the number of bubbles, which itself depends on the oversaturation. In order to determine from the experiments this transfer coefficient by means of the calibration technique the results obtained on the finer scale of Relation (7) are used.
  • Equation (16) h v depends on N 0 : h v ⁇ aDN 0 2/3 S G 2/3 (21)
  • exponent 2 ⁇ 3 results from the surface/volume ratio of the bubbles and it can be modified to take into account of a branched (fractal) shape of the bubbles in the porous medium. Therefore replacement next by a more general exponent d occurs if necessary.
  • This transfer curve h v (S g ) is experimentally determined.
  • the relative permeability used can be the relative permeability of a displacement experiment taken for a saturation of (S g ⁇ S g *). It is then obtained for the gas flow:
  • ⁇ f g 0 ⁇ for ⁇ ⁇ S g ⁇ S g mob
  • f g c ste ⁇ ( S g - S g mob ) ⁇ u o for ⁇ ⁇ S g * ⁇ S g ⁇ S g mob
  • f g c ste ⁇ ( S g * - S g mob ) ⁇ u o + k ⁇ ⁇ k rg ⁇ ( S g - S g * ) ⁇ g ⁇ ⁇ P ⁇ x ⁇ for ⁇ ⁇ S g ⁇ S g * ( 26 )
  • the oil phase being continuous, the Darcy formalism is applied thereto.
  • the relative oil permeability will be determined in a displacement experiment.
  • Equation (27) the pressure appears through the expression of the gas density, the gas being considered to be a perfect gas.
  • FIG. 6 shows simulation examples for a C 1 -C 3 -C 10 light oil. A good agreement is obtained for the various depletion rates. The model has been calibrated on the extreme depletion rates. The same parameters have been used for all of the simulations.
  • FIGS. 7 and 8 show the first series of simulations. In both cases, the rock is the same, but the oils are different. Calibration has been performed on the two extreme rates of FIG. 7 . The same set of parameters has been used for all of the simulations, only S g mob is different.
  • FIGS. 9 and 10 show that there is a good correlation between two series of experiments carried out from two different samples.

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US10/508,206 2002-03-20 2003-03-17 Method for modelling the production of hydrocarbons by a subsurface deposit which are subject to depletion Expired - Lifetime US7343275B2 (en)

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FR0203437A FR2837572B1 (fr) 2002-03-20 2002-03-20 Methode pour modeliser la production d'hydrocarbures par un gisement souterrain soumis a une depletion
FR02/03437 2002-03-20
PCT/FR2003/000841 WO2003078794A1 (fr) 2002-03-20 2003-03-17 Methode pour modeliser la production d'hydrocarbures par un gisement souterrain sousmis a une deplection

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US20070255779A1 (en) * 2004-06-07 2007-11-01 Watts James W Iii Method For Solving Implicit Reservoir Simulation Matrix
US20100082509A1 (en) * 2008-09-30 2010-04-01 Ilya Mishev Self-Adapting Iterative Solver
US20100082724A1 (en) * 2008-09-30 2010-04-01 Oleg Diyankov Method For Solving Reservoir Simulation Matrix Equation Using Parallel Multi-Level Incomplete Factorizations
US20100217574A1 (en) * 2007-12-13 2010-08-26 Usadi Adam K Parallel Adaptive Data Partitioning On A Reservoir Simulation Using An Unstructured Grid
US20110082678A1 (en) * 2009-10-01 2011-04-07 Algive Lionnel Method of optimizing the injection of a reactive fluid into a porous medium
US20160122990A1 (en) * 2014-10-31 2016-05-05 Lavelle Industries, Inc. Flush lever and assembly
US9864098B2 (en) 2013-09-30 2018-01-09 Exxonmobil Upstream Research Company Method and system of interactive drill center and well planning evaluation and optimization
US10318663B2 (en) 2011-01-26 2019-06-11 Exxonmobil Upstream Research Company Method of reservoir compartment analysis using topological structure in 3D earth model
US10584570B2 (en) 2013-06-10 2020-03-10 Exxonmobil Upstream Research Company Interactively planning a well site

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WO2005042920A1 (fr) * 2003-10-30 2005-05-12 Maximino Meza Meza Determination des indices naturels de poussee et de prediction du comportement de l'exploitation future d'un gisement de petrole
JP4603951B2 (ja) * 2005-08-08 2010-12-22 トヨタ自動車株式会社 内燃機関のすす発生量推定装置
CN101366041B (zh) * 2005-12-22 2011-10-12 雪佛龙美国公司 利用溶气驱重油进行储层模拟的方法
US9020793B2 (en) * 2005-12-22 2015-04-28 Chevron U.S.A. Inc. Method, system and program storage device for reservoir simulation utilizing heavy oil solution gas drive
US7983886B2 (en) * 2007-09-10 2011-07-19 Chevron U.S.A. Inc. Methods for performing simulation of surfactant flooding of a hydrocarbon reservoir
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US10119374B2 (en) * 2012-03-12 2018-11-06 Total Sa Method for simulating fluid flows, a computer program and a computer readable medium
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Li et al. Visualization and Numericall Studies of Bubble Growth During Pressure Depletion. Oct. 6, 1991.
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Cited By (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070255779A1 (en) * 2004-06-07 2007-11-01 Watts James W Iii Method For Solving Implicit Reservoir Simulation Matrix
US7672818B2 (en) 2004-06-07 2010-03-02 Exxonmobil Upstream Research Company Method for solving implicit reservoir simulation matrix equation
US20100217574A1 (en) * 2007-12-13 2010-08-26 Usadi Adam K Parallel Adaptive Data Partitioning On A Reservoir Simulation Using An Unstructured Grid
US8437996B2 (en) 2007-12-13 2013-05-07 Exxonmobil Upstream Research Company Parallel adaptive data partitioning on a reservoir simulation using an unstructured grid
US20100082509A1 (en) * 2008-09-30 2010-04-01 Ilya Mishev Self-Adapting Iterative Solver
US20100082724A1 (en) * 2008-09-30 2010-04-01 Oleg Diyankov Method For Solving Reservoir Simulation Matrix Equation Using Parallel Multi-Level Incomplete Factorizations
US20110082678A1 (en) * 2009-10-01 2011-04-07 Algive Lionnel Method of optimizing the injection of a reactive fluid into a porous medium
US10318663B2 (en) 2011-01-26 2019-06-11 Exxonmobil Upstream Research Company Method of reservoir compartment analysis using topological structure in 3D earth model
US10584570B2 (en) 2013-06-10 2020-03-10 Exxonmobil Upstream Research Company Interactively planning a well site
US9864098B2 (en) 2013-09-30 2018-01-09 Exxonmobil Upstream Research Company Method and system of interactive drill center and well planning evaluation and optimization
US20160122990A1 (en) * 2014-10-31 2016-05-05 Lavelle Industries, Inc. Flush lever and assembly
US9803350B2 (en) * 2014-10-31 2017-10-31 Lavelle Industries, Inc. Flush lever and assembly

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US20050165593A1 (en) 2005-07-28
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CA2479361C (fr) 2011-10-11
FR2837572B1 (fr) 2004-05-28
AU2003232292A1 (en) 2003-09-29
WO2003078794A1 (fr) 2003-09-25

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